Variational exact diagonalization method for Anderson impurity models

TL;DR

This paper introduces a variational method for solving Anderson impurity models via exact diagonalization, improving bath discretization and accuracy in energy and observable calculations, applicable to complex multi-orbital systems.

Contribution

The paper presents a novel variational approach that optimizes bath discretization in Anderson impurity models, enhancing accuracy over traditional methods and enabling systematic improvements.

Findings

Accurately reproduces free energies and observables in single orbital models.

Demonstrates applicability to five orbital impurity problems.

Assesses bath discretization schemes within the variational framework.

Abstract

We describe a variational approach to solving Anderson impurity models by means of exact diagonalization. Optimized parameters of a discretized auxiliary model are obtained on the basis of the Peierls-Feynman-Bogoliubov principle. Thereby, the variational approach resolves ambiguities related with the bath discretization, which is generally necessary to make Anderson impurity models tractable by exact diagonalization. The choice of variational degrees of freedom made here allows systematic improvements of total energies over mean field decouplings like Hartree-Fock. Furthermore, our approach allows us to embed arbitrary bath discretization schemes in total energy calculations and to systematically optimize and improve on traditional routes to the discretization problem such as fitting of hybridization functions on Matsubara frequencies. Benchmarks in terms of a single orbital Anderson model demonstrate that the variational exact diagonalization method accurately reproduces free energies as well as several single- and two-particle observables obtained from an exact solution. Finally, we demonstrate the applicability of the variational exact diagonalization approach to realistic five orbital problems with the example system of Co impurities in bulk Cu and compare to continuous-time Monte Carlo calculations. The accuracy of established bath discretization schemes is assessed in the framework of the variational approach introduced here.